Answer:
Step-by-step explanation:
By the trapezoid midsegment theorem,
2x = (x-6) + (2x-8)
2x = x - 6 + 2x - 8
2x = 3x - 14
x = 14
So we know AD = 8, EF = 14, and BC = 20
Answer:
500 lbs of mixed nuts
Step-by-step explanation:
15.4% of mixed nuts = 77 lbs of pecans
Divide the weight of pecans by the percent of mixed nuts to find how many pounds of pecans equal 1% of the mixed nuts:
77 / 15.4 = 5, so 5 lbs equals 1% of mixed nuts
Now multiply that number by 100 to get 100% of mixed nuts:
5 x 100 = 500
Therefore, there are 500 lbs of mixed nuts in a batch altogether.
To check, 15.4% = 15.4/100 = 0.514
Therefore, 15.4% of 500 = 0.514 x 500 = 77
Thereby proving that 15.4% of 500 is 77.
Let one integer be x, the consecutive odd integer is x+2
reciprocals are 1/x and 1/(x+2)
1/x +1/(x+2)=24/143
make the denominators the same:
(x+2)/[x(x+2)] +x/[x(x+2)]=24/143
143(2x+2)=24(x)(x+2)
286x+286=24x²+48x
24x²-238x-286=0
use the quadratic formula: x=22 this doesn't work because 22 is not an odd number.
or x=-2.1666666666 (this is not an integer)
weird.
Answer:
503
Step-by-step explanation:
For an arithmetic sequence, the n-th term is found by
To find 
(the common difference) we can simply subtract one of the terms by the last, for example:
The common difference must be the same throughout the entire sequence, so we can do it once more just to be sure:
We also have to know that 
stands for the first term of the sequence, which in this case is 311.
Now that we know this, let's find the 32nd term
Good luck!
Answer: b
Explanation: cube root is equal to the power of 1/3
Multiply the exponents 24/3=8
